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Search indexed NASA NTRS and DOE OSTI research on propulsion, heat transfer, battery materials and energy systems. Follow report and document links to the original sources.

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At least 37 records · Page 2
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NASA NTRS1984

The magnetopause as a tangential discontinuity for large field rotation angles

Three passes of the ISEE 1 and 2 satellites through the dayside terrestrial magnetopause are discussed where the magnetopause is identified as a tangential discontinuity. This identification is based primarily on the failure of the plasma and magnetic field data to satisfy the conditions for a rotational discontinuity. In all these cases the interplanetary magnetic field was directed strongly southward and the angles between the fields on the two sides of the magnetopause ranged between 136 deg and 170 deg. As this is precisely the field geometry thought to be most conducive for reconnection, the magnetopause would be expected to be a rotational discontinuity. The simplest explanation of this result would appear to be that the magnetic field orientation is not the only factor controlling the onset of reconnection. However, as the identification of the discontinuity applies only locally, it cannot be excluded that for the magnetic field conditions investigated here, different portions of the magnetopause can be described as tangential and rotational discontinuities simultaneously.

Papamastorakis, I.↗
NASA NTRS1987

Interactions of oblique interplanetary discontinuities and their manifestations during STIP intervals 15-19

The generation of slow shock waves as the result of the interaction of Alfven discontinuities with solar wind contact surfaces is considered. The latter are taken to be the boundaries of proton and alpha-particle concentration inhomogeneities. It is found that the intensity of the Alfven discontinuity may be increased as the result of its interaction with the more dense plasma. The converse (i.e., decrease of the Alfven discontinuity's intensity following interaction with a less dense plasma) is also indicated. Also discussed is the generation of a magnetic cloud as the result of the interaction of a quasi-parallel Alfven discontinuity with a dense plasma contact surface. It is shown that the (solar-generated) Alfven discontinuity may then be transformed into non-flare fast and slow shock waves as the result of this interaction. Thus, it is indicated that some fast shock waves in the solar wind may have a nonsolar origin.

Grib, S. A.↗
NASA NTRS1994

A hybrid simulation of contact discontinuity

Contact discontinuities in a collisionless plasma are studied by hybrid simulations, in which ions are treated as particles and electrons are considered as a fluid. It is demonstrated that contact discontinuity with a stable density ramp can exist in cases with a finite electron temperature. An electron pressure gradient is present across the contact discontinuity, leading to the presence of a parallel electric field and hence field-aligned potential increase (Delta Phi (sub parallel)) in the transition region. By reflecting ions at the discontinuity, this parallel electric potential peak reduces the interpenetration between hot and cold ions and maintains a stable density ramp across the contact discontinuity. The ratio of the field-aligned electric potential energy to ion thermal energy, e(Delta) Phi(sub parallel)/kT(sub i), is found to be an increasing function of T(sub e)/T(sub i), where T(sub e) and T(sub i) are respectively the electron and ion temperature.

Wu, B. H.↗
NASA NTRS1997

Computational Considerations for the Simulation of Discontinuous Flows

The numerical study of aeroacoustic problems places stringent demands on the choice of a computational algorithm, because it requires the ability to propagate disturbances of small amplitude and short wavelength. The demands are particularly high when shock waves are involved, because the chosen algorithm must also resolve discontinuities in the solution. In a previous work the capabilities and deficiencies of shock-capturing methods for aeroacoustic problems were demonstrated using a high-order essentially nonoscillatory (ENO) numerical method. It was shown that first-order results are obtained when simulating time-dependent flows with discontinuities. The present study reaffirms this conclusion by comparing the ENO results with those obtained using a conventional linear scheme. A sixth-order-accurate compact implicit finite difference scheme is used to investigate various discontinuous flows. The design order of accuracy is achieved in the smooth regions of a steady-state, quasi-one-dimensional Euler test case, as well as in the time-dependent Burgers' equation. However, in the unsteady Euler sound-shock interaction, first-order results are obtained downstream of the shock. A comparison is made between the linear and nonlinear results, noting the advantages of each method. A discontinuous linear model problem is then used to identify the cause of the first-order results. Here, the nature of the solution error is quantified as being predominantly a numerical phase shift, and a post-processing procedure is demonstrated which increases the solution accuracy downstream of the discontinuity to second-order.

Carpenter Mark H.↗
NASA NTRS1997

Locating the Discontinuities of a Bounded Function by the Partial Sums of its Fourier Series I: Periodical Case

A key step for some methods dealing with the reconstruction of a function with jump discontinuities is the accurate approximation of the jumps and their locations. Various methods have been suggested in the literature to obtain this valuable information. In the present paper, we develop an algorithm based on identities which determine the jumps of a 2(pi)-periodic bounded not-too-highly oscillating function by the partial sums of its differentiated Fourier series. The algorithm enables one to approximate the locations of discontinuities and the magnitudes of jumps of a bounded function. We study the accuracy of approximation and establish asymptotic expansions for the approximations of a 27(pi)-periodic piecewise smooth function with one discontinuity. By an appropriate linear combination, obtained via derivatives of different order, we significantly improve the accuracy. Next, we use Richardson's extrapolation method to enhance the accuracy even more. For a function with multiple discontinuities we establish simple formulae which "eliminate" all discontinuities of the function but one. Then we treat the function as if it had one singularity following the method described above.

Kvernadze, George↗
NASA NTRS2000

Visualization, Extraction and Quantification of Discontinuities in Compressible Flows

Scientific visualizations of two-dimensional compressible flow of a gas with discontinuities are presented. The numerical analogue to experimental techniques such as schlieren imaging, shadowgraphs, and interferograms are discussed. Edge detection techniques are utilized to identify the discontinuities. In particular, the zero crossing of the Laplacian of a field (usually density) is recommended for extracting the discontinuities. An algorithm to extract and quantify the discontinuities is presented. To illustrate the methods developed in the report, the example chosen is that of an unsteady interaction of a shock wave with a contact discontinuity.

Samtaney, Ravi↗
NASA NTRS2000

Discontinuous dual-primal mixed finite elements for elliptic problems

We propose a novel discontinuous mixed finite element formulation for the solution of second-order elliptic problems. Fully discontinuous piecewise polynomial finite element spaces are used for the trial and test functions. The discontinuous nature of the test functions at the element interfaces allows to introduce new boundary unknowns that, on the one hand enforce the weak continuity of the trial functions, and on the other avoid the need to define a priori algorithmic fluxes as in standard discontinuous Galerkin methods. Static condensation is performed at the element level, leading to a solution procedure based on the sole interface unknowns. The resulting family of discontinuous dual-primal mixed finite element methods is presented in the one and two-dimensional cases. In the one-dimensional case, we show the equivalence of the method with implicit Runge-Kutta schemes of the collocation type exhibiting optimal behavior. Numerical experiments in one and two dimensions demonstrate the order accuracy of the new method, confirming the results of the analysis.

Bottasso, Carlo L.↗
NASA NTRS2000

High Order Discontinuous Gelerkin Methods for Convection Dominated Problems with Application to Aeroacoustics

This project is about the investigation of the development of the discontinuous Galerkin finite element methods, for general geometry and triangulations, for solving convection dominated problems, with applications to aeroacoustics. On the analysis side, we have studied the efficient and stable discontinuous Galerkin framework for small second derivative terms, for example in Navier-Stokes equations, and also for related equations such as the Hamilton-Jacobi equations. This is a truly local discontinuous formulation where derivatives are considered as new variables. On the applied side, we have implemented and tested the efficiency of different approaches numerically. Related issues in high order ENO and WENO finite difference methods and spectral methods have also been investigated. Jointly with Hu, we have presented a discontinuous Galerkin finite element method for solving the nonlinear Hamilton-Jacobi equations. This method is based on the RungeKutta discontinuous Galerkin finite element method for solving conservation laws. The method has the flexibility of treating complicated geometry by using arbitrary triangulation, can achieve high order accuracy with a local, compact stencil, and are suited for efficient parallel implementation. One and two dimensional numerical examples are given to illustrate the capability of the method. Jointly with Hu, we have constructed third and fourth order WENO schemes on two dimensional unstructured meshes (triangles) in the finite volume formulation. The third order schemes are based on a combination of linear polynomials with nonlinear weights, and the fourth order schemes are based on combination of quadratic polynomials with nonlinear weights. We have addressed several difficult issues associated with high order WENO schemes on unstructured mesh, including the choice of linear and nonlinear weights, what to do with negative weights, etc. Numerical examples are shown to demonstrate the accuracies and robustness of the methods for shock calculations. Jointly with P. Montarnal, we have used a recently developed energy relaxation theory by Coquel and Perthame and high order weighted essentially non-oscillatory (WENO) schemes to simulate the Euler equations of real gas. The main idea is an energy decomposition under the form epsilon = epsilon(sub 1) + epsilon(sub 2), where epsilon(sub 1) is associated with a simpler pressure law (gamma)-law in this paper) and the nonlinear deviation epsilon(sub 2) is convected with the flow. A relaxation process is performed for each time step to ensure that the original pressure law is satisfied. The necessary characteristic decomposition for the high order WENO schemes is performed on the characteristic fields based on the epsilon(sub l) gamma-law. The algorithm only calls for the original pressure law once per grid point per time step, without the need to compute its derivatives or any Riemann solvers. Both one and two dimensional numerical examples are shown to illustrate the effectiveness of this approach.

Shu, Chi-Wang↗
NASA NTRS2004

Relaxation and Preconditioning for High Order Discontinuous Galerkin Methods with Applications to Aeroacoustics and High Speed Flows

This project is about the investigation of the development of the discontinuous Galerkin finite element methods, for general geometry and triangulations, for solving convection dominated problems, with applications to aeroacoustics. Other related issues in high order WENO finite difference and finite volume methods have also been investigated. methods are two classes of high order, high resolution methods suitable for convection dominated simulations with possible discontinuous or sharp gradient solutions. In [18], we first review these two classes of methods, pointing out their similarities and differences in algorithm formulation, theoretical properties, implementation issues, applicability, and relative advantages. We then present some quantitative comparisons of the third order finite volume WENO methods and discontinuous Galerkin methods for a series of test problems to assess their relative merits in accuracy and CPU timing. In [3], we review the development of the Runge-Kutta discontinuous Galerkin (RKDG) methods for non-linear convection-dominated problems. These robust and accurate methods have made their way into the main stream of computational fluid dynamics and are quickly finding use in a wide variety of applications. They combine a special class of Runge-Kutta time discretizations, that allows the method to be non-linearly stable regardless of its accuracy, with a finite element space discretization by discontinuous approximations, that incorporates the ideas of numerical fluxes and slope limiters coined during the remarkable development of the high-resolution finite difference and finite volume schemes. The resulting RKDG methods are stable, high-order accurate, and highly parallelizable schemes that can easily handle complicated geometries and boundary conditions. We review the theoretical and algorithmic aspects of these methods and show several applications including nonlinear conservation laws, the compressible and incompressible Navier-Stokes equations, and Hamilton-Jacobi-like equations.

Shu, Chi-Wang↗
NASA NTRS2004

Error Analysis for Discontinuous Galerkin Method for Parabolic Problems

In the proposal, the following three objectives are stated: (1) A p-version of the discontinuous Galerkin method for a one dimensional parabolic problem will be established. It should be recalled that the h-version in space was used for the discontinuous Galerkin method. An a priori error estimate as well as a posteriori estimate of this p-finite element discontinuous Galerkin method will be given. (2) The parameter alpha that describes the behavior double vertical line u(sub t)(t) double vertical line 2 was computed exactly. This was made feasible because of the explicitly specified initial condition. For practical heat transfer problems, the initial condition may have to be approximated. Also, if the parabolic problem is proposed on a multi-dimensional region, the parameter alpha, for most cases, would be difficult to compute exactly even in the case that the initial condition is known exactly. The second objective of this proposed research is to establish a method to estimate this parameter. This will be done by computing two discontinuous Galerkin approximate solutions at two different time steps starting from the initial time and use them to derive alpha. (3) The third objective is to consider the heat transfer problem over a two dimensional thin plate. The technique developed by Vogelius and Babuska will be used to establish a discontinuous Galerkin method in which the p-element will be used for through thickness approximation. This h-p finite element approach, that results in a dimensional reduction method, was used for elliptic problems, but the application appears new for the parabolic problem. The dimension reduction method will be discussed together with the time discretization method.

Kaneko, Hideaki↗
NASA NTRS2013

A Floating Node Method for the Modelling of Discontinuities Within a Finite Element

This paper focuses on the accurate numerical representation of complex networks of evolving discontinuities in solids, with particular emphasis on cracks. The limitation of the standard finite element method (FEM) in approximating discontinuous solutions has motivated the development of re-meshing, smeared crack models, the eXtended Finite Element Method (XFEM) and the Phantom Node Method (PNM). We propose a new method which has some similarities to the PNM, but crucially: (i) does not introduce an error on the crack geometry when mapping to natural coordinates; (ii) does not require numerical integration over only part of a domain; (iii) can incorporate weak discontinuities and cohesive cracks more readily; (iv) is ideally suited for the representation of multiple and complex networks of (weak, strong and cohesive) discontinuities; (v) leads to the same solution as a finite element mesh where the discontinuity is represented explicitly; and (vi) is conceptually simpler than the PNM.

Pinho, Silvestre T.↗
NASA NTRS2013

Impedance Discontinuity Reduction Between High-Speed Differential Connectors and PCB Interfaces

High-speed serial communication (i.e., Gigabit Ethernet) requires differential transmission and controlled impedances. Impedance control is essential throughout cabling, connector, and circuit board construction. An impedance discontinuity arises at the interface of a high-speed quadrax and twinax connectors and the attached printed circuit board (PCB). This discontinuity usually is lower impedance since the relative dielectric constant of the board is higher (i.e., polyimide approx. = 4) than the connector (Teflon approx. = 2.25). The discontinuity can be observed in transmit or receive eye diagrams, and can reduce the effective link margin of serial data networks. High-speed serial data network transmission improvements can be made at the connector-to-board interfaces as well as improving differential via hole impedances. The impedance discontinuity was improved by 10 percent by drilling a 20-mil (approx. = 0.5-mm) hole in between the pin of a differential connector spaced 55 mils (approx. = 1.4 mm) apart as it is attached to the PCB. The effective dielectric constant of the board can be lowered by drilling holes into the board material between the differential lines in a quadrax or twinax connector attachment points. The differential impedance is inversely proportional to the square root of the relative dielectric constant. This increases the differential impedance and thus reduces the above described impedance discontinuity. The differential via hole impedance can also be increased in the same manner. This technique can be extended to multiple smaller drilled holes as well as tapered holes (i.e., big in the middle followed by smaller ones diagonally).

Navidi, Sal↗
NASA NTRS2023

Analytical model of foreshock ion interaction with a discontinuity: A statistical study

When a solar wind discontinuity interacts with foreshock ions, foreshock transients such as hot flow anomalies and foreshock bubbles can form. These create significant dynamic pressure perturbations disturbing the bow shock, magnetopause, and magnetosphere-ionosphere system. However, presently these phenomena are not predictable. In the accompanying paper, we derived analytical equations of foreshock ion partial gyration around a discontinuity and the resultant current density. In this study, we utilize the derived current density strength to model the energy conversion from the foreshock ions, which drives the outward motion or expansion of the solar wind plasma away from the discontinuity. We show that the model expansion speeds match those from local hybrid simulations for varying foreshock ion parameters. Using MMS, we conduct a statistical study showing that the model expansion speeds are moderately correlated with the magnetic field strength variations and the dynamic pressure decreases around discontinuities with correlation coefficients larger than 0.5. We use conjunctions between ARTEMIS and MMS to show that the model expansion speeds are typically large for those already-formed foreshock transients. Our results show that our model can be reasonably successful in predicting significant dynamic pressure disturbances caused by foreshock ion-discontinuity interactions. We discuss ways to improve the model in the future.

Terry Z. Liu↗
NASA NTRS1971

Discontinuity stresses in metallic pressure vessels

The state of the art, criteria, and recommended practices for the theoretical and experimental analyses of discontinuity stresses and their distribution in metallic pressure vessels for space vehicles are outlined. The applicable types of pressure vessels include propellant tanks ranging from main load-carrying integral tank structure to small auxiliary tanks, storage tanks, solid propellant motor cases, high pressure gas bottles, and pressurized cabins. The major sources of discontinuity stresses are discussed, including deviations in geometry, material properties, loads, and temperature. The advantages, limitations, and disadvantages of various theoretical and experimental discontinuity analysis methods are summarized. Guides are presented for evaluating discontinuity stresses so that pressure vessel performance will not fall below acceptable levels.

Source record↗
NASA NTRS1972

Comment on the large velocity discontinuities in the solar wind

Ivanov (1970) showed that rotational discontinuities can exist in an anisotropic medium, and claimed that 10 of the 11 discontinuities examined by Burlage (1969) are rotational in Hudson's sense. Using Hudson's (1970, 1971) data, it is argued that at least 5 of the 10 discontinuities are of the tangential and not rotational type. This supports Burlaga's interpretation, according to which there exist tangential discontinuities characterized by large shifts.

Burlaga, L. F.↗
NASA NTRS1974

Method and device for detection of surface discontinuities or defects

Surface discontinuities of defects such as cracks and orifices are detected by applying a penetrating fluid, preferably a liquid, to a test surface so as to cause the liquid to penetrate any minute cracks or opening in the surface, removing the excess liquid from the surface, and leaving a residual in the discontinuities, cavities, or in the subsurface materials. A sheet of porous material impregnated with a sensitizing medium which will react with vapors of the residual liquid to form a visible pattern is applied to the test surface. The residual liquid trapped in the discontinuities, cavities, or subsurface material is vaporized, and, as the vapors contact the sensitizing medium on the sheet, a pattern corresponding to the discontinuity is formed on the sheet material and the penetrant completely removed from the sample.

Leger, L. J.↗
NASA NTRS1983

Rotational discontinuities and the structure of the magnetopause

Symmetric and asymmetric rotational discontinuities are studied by means of a one-dimensional computer simulation and by single-particle trajectory calculations. The numerical simulations show the symmetric rotation to be stable for both ion and electron senses of rotation with a thickness of the order of a few ion gyroradii when the rotation angle of the tangential field is 180 deg or less. Larger rotation angles tend to be unstable. In an expansive discontinuity, when the magnetic field on the downstream side of the discontinuity is larger, an expanding transition layer separating the highfield from a low-field region develops on the downstream side, and a symmetric rotational discontinuity forms at the upstream edge. The implication of these results for magnetopause structure and energy flow through the magnetopause is described.

Swift, D. W.↗
NASA NTRS1985

Alignment of velocity and field changes across tangential discontinuities in the solar wind

Three-dimensional IMP 8 and Voyager 2 plasma and field data are used to investigate the relative changes in direction of the velocity and magnetic field vectors across tangential discontinuities in the solar wind. It is found that Delta-v and Delta-B/rho exp 1/2 are closely aligned either parallel or antiparallel to each other in the sense associated with the propagation of Alfven waves or rotational discontinuities outward from the sun. This alignment is observed at all solar distances betwen 1 and 2.2 AU and is independent of the solar wind stream structure. Several possible causes of the effect are briefly discussed, including interplanetary turbulence, the propagation of large-amplitude Alfvenic fluctuations traveling independently through the solar wind on both sides of the discontinuities, and the propagation of surface waves on tangential discontinuities.

Neugebauer, M.↗